Applications of polynomial functions

Lessons

1. A piece of cardboard is 15 cm in length and 8 cm in width. To make a box without lid with this cardboard, 4 identical squares with a side length $x$ are cut out from the corners, and then, the sides are folded up.
   
   i)
   Express the volume, $V$, in relation to $x$ in a polynomial function.
   ii)
   Find the domain by graphing the function.
   iii)
   In order to maximize the volume, what should the side length of each cut-out square be?
   iv)
   Determine the maximum volume.
   v)
   Find the dimensions of the box. Round your answer to 1 decimal place.
2. Dave and 3 of his friends all have their birthdays on October 10. Dave is 4 years older than Emma. Yet, he is 2 years younger than Frank, and 10 years younger than Gary. Last year, on October 10, the product of their ages was 65 501 larger than the square sum of their ages. How old was Dave last year on his birthday?